Publicação: An exact equation for the free surface of a fluid in a porous medium
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Data
2007-01-01
Orientador
Coorientador
Pós-graduação
Curso de graduação
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Editor
Siam Publications
Tipo
Artigo
Direito de acesso
Acesso aberto
Resumo
We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.
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Inglês
Como citar
Siam Journal on Applied Mathematics. Philadelphia: Siam Publications, v. 67, n. 3, p. 619-629, 2007.
